Method of cutting gears



1944. E. WILDHABER 2,357,153

METHOD OF CUTTING GEARS Original Filed Dec. 22, 1957 6 Sheets-Sheet l1944. E. WILDHABER 2,357,153

METHOD OF CUTTING GEARS Original Filed Dec. 22, 1957 e Sheets-Sheet 2ERNEST W/LDf/HBER Aug. 29, 1944. E. WILDHABER METHOD OF CUTTING GEARSOriginal Filed Dec. 6 Sheets-Sheet 4 Aug. 29, 1944. E. WILDHABER METHODOF CUTTING GEARS Original Filed Dec. 22, 1937 6 Sheets-Sheet 5 /N VE/VTOR R 5 w H 0 M w T 5 m E 9, 1944. E. WILDHABER 2,357,153

METHOD OF'VCUTTING GEARS Original Filed Dec. 22, 1937 6 Sheets-Sheet 6INVENTOR .ERNEST W/L DHH 55 213 Z0 W244i ATTORN" Y roughing blade.

Patented Aug. 29, 19

Ernest Wlldhaber, Brighton, N. 1., asslgnor to Gleason Works, Rochester,N. Y., a corporation of New York Original application December 22, 1937,Serial No.

. 181,177, now Patent No. 2,267,181, dated December 23, 1941;\ Dlvldedand this application October 9, 1940, Serial No. 360,437

3': Claims.

The present invention relates to the manufacture of gears andparticularly to the manufacture of straight tooth bevel gears. Broadlyconsidered the invention comprises a new form of gearing, a novel methodof manufacturing gears, and a new and improved form of gear cuttingtool. The present application covers the new method and is a division ofmy copending application, Serial'No. 181,177, filed December 22, 1937,now Patent No. 2,267,181, granted December 23, 1941.

In general, the method of the present invention is an improvement overthe method of cutting gears described in my earlier co-pendingapplication No. 164,340, filed September 17, 1937, now Patent No.2,315,147, granted March 30, 1943. In my vearlier application a methodof cutting straight bevel gears is disclosed in which a disc-type gearcutter is employed and tooth spaces of the gear are cut by rotating thiscutter in engagement with a tapered gear blank while holding the blankstationary on its axis and while producing a relative feed movement beitis possible to successively rough and finishcut a tooth space of a bevelgear on each revolution of a cutter. Thus a cutter may be used that hasa plurality of roughing blades followed by a plurality of finishingblades with a gap between the last finishing blade, and the first Withsuch a. cutter, a tooth space may be roughened during feed of the cutterin one direction across the face of a gear blank and this same. toothspace may be finished during the return feed motion of the cutter, andthe blank may be indexed when the gap in the cutter is abreast of theblank.

- The method of cutting bevel gears disclosed in my prior applicationNo. 164,340 is, therefore, very fast. The cutter used, however, isdifllcult and expensive to manufacture, since each finishing blade ismade to a different profile shape to cut at a different point along thelength of 'a gear tooth. Moreover, the method is strictly a -highproduction process since the cu'tter'is made primarily to cut a givengear only.

A primary object of the present invention is to provide a method ofmanufacturing bevel gears which will have all of the advantages of themethod of my earlier application referred to, but which will permit ofemploying a simpler and less costly form 0! cutting tool.

Another object of the invention is to provide a method of cutting gearshaving all the advantages of my described prior process, but in which a.given cutter may be used to cut a con-- siderable range of work.

A still further object of the invention is to provide a method ofcutting gears which will permit of simultaneously roughing andfinish-cutting in two adjacent tooth spaces of a gear blank and whichwill, therefore, be even faster than any heretofore employed, but whichwill nevertheless permit of using relatively simple cutting tools. a

Other objects of the invention will be apparent hereinafter from thespecification and from the recital of the appended claims.

With the present invention, the tooth spaces of a gear are cut,-as in myearlier process, by rotating a disc-type cutter in engagement with a.gear blank while simultaneously feeding the cutter "relatively acrossthe face of the blank, but a cutter is employed whose finishing cuttingblades have corresponding side cutting edges of identical profilecurvature." Preferably the'cutter used has side cutting edges ofcircular arcuate profile and, forcutting bevel gears, a cutter is usedthat has the centers of vcurvature of the profile of successive bladesdisplaced from one arranged only part way around its periphery another.When such a cutter is 'rotated in engagement with a tapered gear blankand simultaneously fed lengthwise of the blank, successive blades willcut a. bevel gear tooth having the desired change small end.

As in the method of my prior application, No. 164,340, the cutteremployed in the process of the present invention may have its cuttingblades in shape from its large to its with a gap between the last andfirst blades and the blades may be all roughing blades, or' allfinishing blades, or part roughing and part finand indexed when the gapabreast of the cutter.

uniform displacement of the profile centers of successive blades, thedesired variation in pro-- file curvature of the gear teeth can beobtained by feeding the cutter at a uniform rate along the length of thegear teeth as the cutter rotates in engagement with the blank. Byvarying the rate of feed, however, in either form of cutter, a singlecutter can be used to out different bevel gears.

For gears of coarse pitch, it is preferred to use 'separate cutters forroughing and finishing, but

both operations may be carried on simultaneously. Thus, a pair ofcutters may be employed, one a standard stocking cutter for roughing outthe tooth slot, and the other a finishing cutter, such as previouslydescribed, for finishing the previously roughened out tooth slot. Thetwo cutters may be mounted coaxially to operate in adjoining toothspaces and both may be fed simultaneously together across the face ofthe blank while being rotated in engagement with the blank.

Bevel gears out according to the present invention will have inherentlya desirable localization of tooth bearing or contact, but the amount oflocalization of bearing may readily be modified by applying theprinciples of my prior Patent No. 1,733,326 of October 29, 1929, in thecutting of the gears.

Several different embodiments of the invenfurther explanatory oi thebasic principles of the invention:

Fig. 12 is a diagrammatic view showing a bevel pinion in section andillustrating atically the motions employed in the cutting of the sameaccording to the pruent invention;

Fig. 13 is another sectional view of-this pinion. illustratingdiagrammatically the type of chips cut by a cutter in the process of thepresent inventlon;

Fig. 14 is a side elevation of a cutter such as may be-employed incutting gears according to the method of the present invention:

' P18. 15 is a sectional view of this cutter taken ontheline lt-il ofFig. 14: 1

.Fig. 16 is a diagrammatic view showing one of the roughing blades ofthis cutter superimposed upon a finishing blade; 7

Fig. 17 is a fragmentary diagrammatic view showing how separate roughingand finishing cutters may be employed simultaneously in a modificationof the present invention to rough tion are illustrated in theaccompanying drawings in which:

, Fig. l is a fragmentary diagrammatic elevational view and Fig. 2 is afragmentary diagrammatic sectional view showing one form of cutter whichmay be employed in practicing the present invention;

Fig. 3 is a diagrammatic view showing ter in the operation of cutting atthe large end of a tooth space of a tapered gear;

Fig. 4 is a diagrammatic view showing this cutter in the operation ofcutting at the small end or the tooth space of this tapered gear;

Fig. 5 is a fragmentary sectional view of the gear on a somewhatenlarged scale taken on the line 5-5 of Fig. and illustratingdiagrammatically certain principles underlying the present invention;

Fig. 6 is a fragmentary axial sectional view of a bevel pinion madeaccording to this invention, further illustrating diagrammaticallycertain principles of the present invention;

Fig. 7 is a fragmentary axial sectional view of the bevel gear which isto mate with the pinion shown in Fig. 6, and illustrating how the pairmay be made conjugate when both members are produced according to themethod of the present invention;

Fig. 8 is a diagrammatic view illustrating on' a .somewhat enlargedscale the construction of a cutter such as may be employed in theprocess of the present invention;

Figs. 9 to 11 inclusive are c this-cutviews is and finish-cutsimultaneously separate tooth slots of a gear blank;

Fig. 18 is a diagrammatic view illustrating the structure and operationof the roughing cutter shown in Fig. 17; and

Figs. 19 and 20 are diagrammatic side elevational views, respectively,of the roughing and finishing cutters shown in Fig. 1'7, and furtherillustrating the construction of these tools.

In any bevel gear it is desirable to have the teeth and the tooth spacestaper in depth and width from their outer to their inner ends so thatthe teeth of the gear may be of substantially uniform strengththroughout their length.

The method of the present invention permits of making bevel gears whichhave these desirable characteristics. The principles on which thisinvention rests will now be discussed.

In Figs-3 to 6 inclusive, I0 denotes a bevel pinion cut bythe process ofthe present invention. The axis of this pinion is designated at 12 andits apex at 25. As will be seen clearly in Fig. 6, the teeth 2| of thispinion decrease in depth from their outer to their inner ends and, aswill be seen from comparison of Fig. 4 with Fig. 3.

the teeth and the tooth spaces of this pinion decrease in width fromtheir outer to their inner ends and the profile shape of the teeth alsochanges correspondingly from end to end, The sides of the teeth at thesmall end are more curved than at the large end.

In Figs. 5 and 8 the points? and P' are mean points in the oppositesides of a tooth space of the pinion 20. The planes 2s and 24 aretangent, respectively, to the opposite sides of this tooth space atthese mean points P and P. As will be obvious, if the teeth and toothspaces of this pinion are to taper in width and height from end to end,the planes 24 and 24' must pass through the apex ll of the pinion andintersect ii: a line as which also passes through this apex 2Disregarding, at first, the bottom 28 of the tooth space, it willreadily be seen that the V- shaped profile formed by the tangentialplanes 24 and 24' could be swept out with a milling cutter having aV-shaped cutting profile, by feeding that milling cutter in thedirection of the line 28-, The tooth bottom 28, which is inclined to theline of feed 28, can then be cut by making the than those which areadapted to cut at the large asemss tooth space. This-spiral will be 'anlnvolute on' cutters which are fed across theface of the blank at auniform rate.

Now the tooth'space which is to -be produced on the pinion I doesnothave a V-shaped pro-' file, such asis formed by the tangential planes 24and 24, but it is formed by-opp'osite side tooth surfaces 30 and 30'which are of convex profile and the profile curvature of these toothsurfaces varies, moreover, from end to end. reproduce the desired convextooth profiles 39 and 30', a

cutter is employed that has concave side cutting edges. If thesecuttingprofiles were arranged at a constant radial distance from thecutter axis, as on conventional milling cutters,- then the toothsurfaces produced would have straight line elements parallel to the lineof feed28. What I desire to produce, however, is a bevel pinion 20having tooth surfaces with substantially straight tact between thecutter-surface and the tooth surline elements 33 that extend through thecone apex 29 of the gear. This .can be obtained by using a cutter inwhich the centers of curvature of the opposite side cutting edges ofsuccessive blades are displaced from one another in the direction of thetangents 24 and 24' (Fig. 2).

Referring now to Figs. 1 and 2, it will be seen that here is showndiagrammatically a,cutter which has corresponding side-cutting edgesthat are of identical curvature and that have their centers of curvaturedisplaced from one another in the direction of the tangents 24 and 24.The axis of this cutter is denoted at '36. 31 ,is the center of theprofile of the cutting edge of that blade of the cutter which is to cutat the mean point P in the pinion tooth surface 30. 38 and 39 are thecenters of curvature of the cutting edges of blades which are spacedfrom the mean blade angularly about the periphery of the cutter atpoints suitable to cut at the large and at the small ends of the toothsurface 30, respectively. The centers 38 and 39 are displacedequidistantly from the center 31 along a line 40 which is parallel tothe tangent plane 24. When a cutter is employed in which the cuttingprofile centers 38, 31, 39, etc., are displaced uniformly from oneanother, asillustrated, tooth surfaces will be produced on the pinionwhich will contact with the tangential plane 24 along a straight lineinclined to the direction of feed 25. It will readilybe understood,then, that by employing a' cutter, which is constructed so that theprofile centers of successive blades are displaced at a suitable ratefrom one another, any desired straight line of contact between thecutter and the tooth surface being cut may be arrived at, such as theline 33 (Fig. 6) which extends to the pinion apex 25.

With a. cutter such as described up to this point, however, we stillwould only get tooth surfaces of substantially constant profile shape'along the length of the gear tooth. What we want to obtain, however,are gear profiles on the gear teeth which are increasingly curved fromthe large to the small ends of the teeth.

-In the cutting of the gear according to this invention, as alreadydescribed, the cutter rotates on its axis and is simultaneously movedrelatively along the length of the gear tooth space being cut. Therelative cutting motion is, then, as if a circle 43 (Figs. 1 and 6)concentric with the cutter axis 36 were rolling on a straight line 44parallel to the line 26. 45 is the instantaneous axis of this rollingmotion. The line of instantaneous conthan the center of the profile ofthe cutting edge respectively, spaced equidistantly from the mean facefinished thereby is subject to the require ments of gear contact and isa projection of the instantaneous axis to the cutter surface. Point Pisapoln projection and the line of conmus c agline 43 inclined to theradial plane 41 of utting surface of the cutter.

inasmuch as th'ecuttirig surface of the cutter and the tooth'surfao'ebeing produced thereby contact along the inclined line 49. theprofilesof I the cutter surface and of the tooth surface in a radialplane 41 of the cutter are bound to dlifer from one another. A concavecircular cutting profile 48 (Fig. 2) having a radius 49 and a center 31will produce, therefore, a tooth profile 50 which is more curved thanthe cutting profile 49 and which has a radius 5! and a curvature center52-. The difi'erence in curvature between the cutting surface and thetooth surface, which is to be produced, increases with increasing cutterdiameter and also with increasing inclination of the element 33 of thetooth surface to theclirection of feed 26.

It is now apparent that a given cutting profile 48,,(Fig. 2') willproduce increasingly curved tooth profiles the faster its center isdisplaced along the .line 40 parallel to the tangent plane 24 and thevention, then, a cutter will be used in which the centers of curvatureof successive cutting edges are displaced at avarying rate, instead ofat a uniform rate, along the line 40 parallel to the tooth surfacetangent 24. In such a cutter, the center of profile of the cutting edge,which cuts at the small end of the pinion tooth, will be displacedfurther along the line 40 from the mean center 31 which cuts at thelarge end of the pinion tooth. Thus, instead of having centers of theprofiles of the cutting edges, which cut at the small and at the largeends of the tooth, located at 39 and 38,

center 31, a cutter will be employed in which the centers of the cuttingedges of these blades, which cut at the small and the large ends ,of thetooth, respectively, will be at the 'points 39 and 38', respectively,spaced non-uniformly from the mean center 31.

In Figs. 3 and 4, 4| and 42 denote, respectively, the blades which cutat the large and small ends of the tooth space. The radius of curvature49 of the side cutting edge 53 (Fig. 3) of the blade H, which cuts atthe large end of the tooth space, is the same as the radius of curvature49 of the side cutting edge 54 (Fig. 4) which cuts at the small end ofthe tooth space, and it will be the same as the radius of curvature 49of the mean cuttingone another at a non-uniform rate in the direction ofthe tangent 24 as already stated. The centersof curvature of the cuttingedges of other blades which cut at other points along the length of thetooth space, are disposed between the extreme positions 39' and 38 andnon-uniformly spaced from one another. The centers of the profiles ofsuccessive cutting edges of the cutter are arranged, then, on a conicalor three-dimensional spiral, coaxial with the axis 30 of the cutter. Thelead of this spiral becomes increasingly larger for the cuttin edgeswhich are coordinated to the small end of the pinion tooth so that theprofile produced at the small end of the pinion tooth may be much morecurved than the cutting edge which cutsthat end of the tooth. On theother hand,

at the large end of the pinion tooth, the tooth,

employed, the line of contact iIP-l between the tooth surface and thetangential plane 24 is no longer a straight line but becomes a curve, H5whose concave sidefaces the tooth bottom 20. The curve is shownexaggerated in the drawings. What has been said about one side It of thepinion teeth applies equally, of course, to the other side of the pinionteeth. Hence, by use of a suitable cutter, both sides of a tooth spaceof a tapered gear may be cut simultaneously according to the method ofthe present invention to taper both in depth and width. In Fig. 2, I9",31'', 38" denote, respectively, the centers of profile curvature of theside-cutting edges which are to cut at the small end, center and largeend, respectively of the tooth surface The centers 38", 31" and 39"correspond for one side of the cutter to the centers 38, 31 and 38' forthe opposite side of the cutter. Likewise,

49" and ii", respectively, are the radii of curvature of the cuttingedge 48 and of the tooth profile 50" cut thereby, corresponding in thisrespect to the radii l9 and BI, respectively, and the profiles l8 and50, respectively.

For cutting the pinion 20, then, a cutter will be used, such as shown inFigs. 1 and 2, which has cutting blades, whose top cutting edges arearranged in a spiral 51 about the axis 86 of the cutter, and whose sidecutting edges are of uniform circular arcuate curvature but have centersof curvature displaced progressively from one another radially andlaterally along a spiral of varying lead. When this cutter is rotated inengagement with the gear blank and simultaneously fed across the face ofthe blank, it will produce tooth surfaces whose profile curvatureschange in the desired fashion from the large to the small ends of theteeth and whose depth varies in the desired fashion from thelarge to thesmall ends of the teeth.

The gear 60 (Fig. 7), which is to mate with the pinion 20, may be cut inthe same way as the pinion 20. BI is the axis of this mate gear '0. 62its apex, and 63 a straight line element .of its pitch surface. The line65 denotes the line of contact between the cutting surface of thecutter, which is used to produce the gear 60, and the tooth surface 66cut thereby. P is again a mean point of contact between the cuttingsurface and the tooth surface to be cut, and 61 is the line of contactbetween the tooth surface and a plane tangent to said surface at saidmean point P. This line of contact 81 is again a curved line and facesthe bottom 68 of the tooth space. Hence, when a. pair of gears 2| and60, out according to the method of the present invention, are in mesh,the lines of contact H5 and 61 of the mating tooth surfaces with acommon tangent plane will be oppositely disposed withofagearpairinsuchawayastoobtaintooth surfacesonthetwo members ofthepairwhole line elements are inclined to one another ac-' cording to theprinciples laid down in my prior United States Patent No. 1,733,328 towhich reference has already been: made above.

In the cases described it will be noted that the line of instantaneouscontact between the cutting surface of the cutter and a tooth surfacefinished thereby is inclined to the radial plane of the cutter. Theinclination is usually in excess of 30 and it is in the same directionon both sides of a tooth space. The lines of contact on both sides ofthe gear teeth extend from the bottom of the tooth at the small endthereof toward the top of the tooth at the large end thereof. On gearsof standard proportions, the inclination of these lines of instantaneouscontact to the radial plane of the cutter is particularly marked on thepinion, because of the long addendum ordinarily used on bevel pinions.0n the gear where the tangents to the opposite sides of a tooth spaceusually include a smaller angle with each other than on the pinion, theline of instantaneous contact is often so much inclined to a radialplane ofthe cutter that it departs only slightly from the generaldirection of the tooth surface.

The cut made by each individual cutting edge of a cutter nearlycoincides with the line of instantaneous contact, particularly when alarge number of cutting edges is provided. In any case, thecharacteristics stated for the lines of instantaneous contact are truealso for the cuts of the individual cutting edges. fore say that thetooth sides of a gear produced according to the present invention aresurfaces enveloped by a suitable number .of concave cuts, which extendin a general direction from the bottom of the tooth surfaces at thesmall end upwardly and backwardly toward the large end of the tooth onboth sides of a tooth space. It should be noted that the cuts areinclined to the lines of instantaneous gear contact so that smooth toothaction is obtained when a pair of gears, which have been out accordingto this invention, are rolled together, even though the number ofcutting edges in the cutter be relatively small and the tooth surfacesproduced consequently contain cutter marks.

Fig. 8 further illustrates diagrammatically the structure of a cuttersuch as may be employed in the cutting of gears according to the presentinvention. The cutting surface of the cutter contains a basic V-shapedcontour formed by the tangents T and T. The side cutting edges have abasic circular profile of constant radius. The opposite side cuttingedges which operate We may thereat a mean point along the length of thetooth space are denoted at I and I00, respectively. In the view I haveshown superimposed upon these, the cutting edges IOI, IOI' and I02, I02,respectively, which cut at the large and small ends of the tooth space,respectively. The center of the cutting edge I00 is denoted at I03. Thecenter of the cutting edge IOI is at I40 and the center of the cuttingedge I02 is at I00.

The several cutting edges IOI, I00 and I02, have, of course, equal radiiI04 but the centers I03, I03, I00, respectively, of curvature of thesecutting edges are displaced from one another in the direction of theline I0I. It will be noted, too. that the heights of the blades vary.This is to obt the desired taper in depth of the tooth space from oneend to. the other. Thus the tip .of the cutting blade, which cuts at.the large end of the tooth space, is denoted at IIO, the tip of theblade, which cuts at a mean point along the length of the tooth space.is denoted at III, and the tip of the blade, which cuts at the small endof the tooth space. is denoted at 2. It will be observed that the bladewhich cuts at the small end of the tooth space is of greatest height;The tip cutting edges of the blades of the cutter are arranged in aspiral, as already described, which is coniugate to the tooth spacebottom which is to be produced.

I have already pointed out that the line of instantaneous contact 43(Figs. 1 and 6) between the cutter and the tooth surface is obliquebecause it is the normal projection of instantaneous axis 43 to thecuttingsurface. While this can be verified with the known methods ofdescriptive geometry, I shall add nevertheless an analysis which givesclosely approximate results more directly. Figs. 9 to 11 inclusive areextremely or infinitely enlarged views of the tangential plane 24 to thetooth surface 2| of the gear 20 at the mean point P. Line II3, extendingthrough points P and H4, is the line in the cutting surface of thecutter which corresponds to line P-- of the tooth surface (Fig. 6). LineII3 appears as a straight line in the enlargement shown. Line I I3 and 0equal to distance 30-45, I obtain in known manner:

' r'tan 6'=c tan 6 tan 6 tan 6 The cutting surface in the immediatevicinity of the point P can be described by bodily moving theradialcutting profile of the cutter along the line 3 while at the sametime moving it slightly along 24 (Fig. 5) 'so that the profile point atline- III remains continuously in contact with the conical cuttingsurface described by the profile tangent. In other words, the ordinate zof any point of the cutting surface above the tangential plane can beconsidered as composed of the ordinates of the cylindrical surfacedescribed by moving the radial. cutting profile along tangent II3 and ofthe ordinates of the conical surface described by the'profile tangent 24when rotated about the cutter axis. The resulting ordinate is thedifference between the two individual ordinates.

In our present second-order approximation, the conical surface oftangent 24 departs from the tangential plane at P like a cylindricalsurface having the same straight line element at P and the same normalradius r (Fig. 2) as readily understood. The normal radius r' is thedistance P-III (Fig. 2) of the point P from the cutter axis measuredalong the normal to the cutting surface. I I1 i the point ofintersection of the normal with the cutter axis 30.

What is true of the ordinates z is also true of their derivatives, thatis, of the inclination of the normals to the cutter surface. Thesesurface normals may be plotted as vectors and geometrically added assuch.

Take a point I 20 (Fig. 9) having a distance a: from the line I2I'and adistance 11' from the line H3. The normal at I20 to the conical orcylindrical surface extending along the line I2I is inclined at an anglewhose tangent:

is inv a direction parallel to line H6 and perpendicular to line I2 I.

Let C denote the radius of the profile of the cutting surface in aradial plane of the cutter, that is, substantially the radius of theside cutting edges of the cutter, that is, the distance 49 (Fig. 2). LetR equal the curvature radius of the produced tooth surface in a normalsection passing through the mean point P and the perpendicular to itsline of contact II! (Fig. 6) with the tangential plane at P.

The radius of the cylindrical surface extending along the line I I3 isthen 0 cos 6' I I: C.cos 6' and y (y-a: taut) cos 6 where y is theordinate of the point I20 with reference to line H6 and a: is theabscissa.

Through transformation,

y y-z tan 6' Leos "'C'.cos 5 C This gives the vector ordinate. Thevector abscissa is equal'to r 1.8m sw gg 1151+;

The vector components, when geometrically added, give a resultant I, seeFig. 9, which describes the direction and inclination of thesurfacenormal at point I20.

At the line of contact 46 (Figs. 2, 6 and 10) the normals of the cuttersurface and the produced tooth surface coincide. Accordingly both thedirection and amount of inclination of the normals must be the same onboth the cutting surface and on the tooth surface produced.

Hence: the ratio of the vector abscissa to the vector ordinate is equalto tan y-l''gz 'gw and to tan 8 where w is the angle between the line ofcontact 46 and the line of feed I ll.

(tan 6-tan 6') (tan w-tan 6') t The vector ordinate or ordinatecomponent of the inclination of the normal of the produced tooth surfaceis tan w= (11- an a) f;

I It must be equal to the ordinate component given above, that is, equalto I zanii =(u ztm6) c056 is here the radius of curvature of the geartooth profile in a section perpendicular to the direction of feed, thatis, in the same section in which the radius C, equal to 49 (Fig. 2), istaken.

It is known how cos 6 the radiusof profile curvature, should changealong the teeth of a bevel gear. Accordingly, we determine first thenormal radius r and the rate of feed of the cutter along the length ofthe gear tooth from the normal requirements, and then change tan 6 alongthe gear tooth Just enough to obtain the desired difierent profile radiiat various points along the tooth.

The above Formula (3) therefore enables us to arrive at the rate ofchange of tan 6 and therefore at the required curvature of the line i I.

At the mean point P (1'18. 11) we Provide an inclination 6 as arrived atfrom the requirements of tooth design and lengthwise mismatch of thetooth surfaces of mating gears. At point 66 (Figs. 6 and. 11) nearer tothe large end of the tooth, we provide a smaller inclination of thetansent I26 so that the tooth profile curvature dilfers less from thecurvature of the cutting edge which produces the same. At point llnearer to the small end of the gear-tooth, the incllnation'of thetangent ifl'is made larger than the inclination of the mean tangent illso that the tooth profile produced is more curved than the cutting edgewhich produces the same.

In the embodiment of Figs. 1 to 3 inclusive, a profile curvatureradius va where a' is the inclination at the mean point P.

- According to Formula (3a), the change in R cos 6 5 d (tan' 6) r (l-.z.-

Then

38.11 6 d tan 6) 3! -a -2 tan 5 Accordingly,

c ll= l r 7) 2 tan 6 dz cos 6 (A cos 6) n: R dz (cos 6) r (1-:-) -2A sin6 The radius of curvature of the line H6 may readily be determined fromthe above term L as and ordinarily will be found to be so large as to behardly noticeable to the eye.

iormulas. In both cases, the feed illustrated by the rolling circles 43and 43', respectively, is uniform, that is, in direct proportion to thecutter rotation. I

It is within the contemplation of theinvention, however, to employ anon-uniform feed, also, where desirable. In this case the lead of thecircular cutting profiles along the tangent 24 (Fig. 2) may be madeuniform, that is, the centers of curvature of equi-spaced blades of thecutter may be also equally spaced from one another as indicated at 38,31 and 39. In other words, we can achieve the same results, with avarying feed rate and a cutter whose successive cutting edges have theircenters of curvature displaced uniformly from one another, as we canobtain from a constant feed rate and a cutter whose successive cuttingedges have their centers of curvature displaced at a varying rate fromone another. The reason is apparent from Formula (3b). Where the rate ofdisplacement of the center of successive cutting edges of the cutter isuniform, tan a is constant, but c is variable. may therefore bedetermined for various points along the tooth to give the desiredprofile radius. The feed rate required varies like 0 along the tooth aswill be readily understood.

A further embodiment of the invention resides in th combination of thetwo modifications already described. The cutter may have cutting edgesthe centers of curvature of whichare displaced at a changing rate fromone another and,

such a cutter may be fed along the gear tooth being cut at a variablefeed rate. This embodiment of the invention has the advantage that therange of a given cutter is increased so that the same cutter may be usedfor cutting a wide variety of gears. However, either of the twoembodiments of the invention first described have considerable range ofuse, for a given cutter may be made to cut gears of different toothconformation simply by changing the rate of feed of the cutter along thetooth.

Because of the possibility of varying the rate of feed of the cutter asit moves along the gear tooth, the invention may be employed withdistinct advantage also in the cutting of cylindrical gears such as spurand helical gears, because with the cutter and the method of the presentinvention it is possible to obtain any desired amount of localization oftooth bearing on such gears.

The cutter used for spur gears may have the centers of the correspondingside-cutting edges of successive blades arranged on a spiral of uniformlead. Such a cutter will sweep out a cylindrical surface which isinclined to the pitch surface of the spur gear being cut. By using theprinciples of my prior patent above mentioned, then, a pair of spurgears may be out which will mesh with localized tooth bearing.

The feed alon the teeth of tapered gears during the finishing cut isconsiderably longer than the face width of the gear being cut. This is.vides higher accuracy and improved finiih on the tooth surface beingproduced.

The preferred meth'odof cutting gears accord-- ing to this invention bysuccessive roughing and finishing cuts will now be described in moredetail. This method broadly may be applied in the use of any disc-typerotary cutter which is constructed to perform a single revolution perfeed cycle. Thus this method is applicable also to the cutters describedin my pending application No. 164,340 above mentioned.

In Fig. 12, I40 denotes a. bevel gear or pinion s which is to be cut. Iis the center or axis of the cutter, which is employed in the cutting ofthis gear, when the cutter is operating at a mean point along the lengthof a tooth I42 oi the gear.

The dotted line I43 denotes the spiral tip surface of the cutter whenits center is at the mean position I. The cutter is assumed to beturning continuously in the direction of the arrow I45 during thecutting operation and in the finishing operation such relative feedmovement is produced between the cutter and the gear blank as if thecircle I41 circumscribed about the axis I of the cutter were rolling ona line I40 which is parallel to the direction of feed I49 and inclinedslightly to the bottom I50 of the tooth space being cut. For the cuttingoperation, the gear blank I40 is adjusted to an angle with respect tothe direction I49 of feed smaller than its root angle. I

I52 denotes the line of instantaneous contact between the cutter surfaceand the finished tooth surface of the gear in the mean position. Tocompletely finish the tooth surface, the finishing cut is started withthe cutter positioned so that its center is at HP and the cutter is fedacross the face of the blank as it rotates on its axis, until its axisreaches the position MI". The -.lines of contact I52 and I52",respectively, which correipond to the cutter-axis positions Hi and MI,respectively, Just reach the tooth surface I42 at opposite ends thereof.In actual practice, it is necessary to feed the cutter at both ends farenough to permit reversal of the direction of feed without shock. In theextreme positions of feed movement of the cutter, then, the cuttercenter; would attain positions such as Mia and I4 lb to permit offinishing between positions I4 I and HI" at a uniform rate of feed.

The cutter may be made to finish out only. In this case, it would haveno rough-cutting edges and in this case the return feed from theposition I4Ib to the starting position I4 la may be effected veryrapidly. The indexing of the gear may be performed during this returnmovement while the gap in the cutter is abreast of the gear blank.Preferably, however, the cutter is provided with roughing as well asfinishing blades so that it may successively rough and finish cut atooth space in a single revolution. The roughing operation is thenpreferably partly or wholly performed during feed of the cutter from aposition I4Ibto the position Mia and the finishing cut takes placeduring return movement from the position I4Ia to the position lb. Thegear is indexed, as before, when the gap in the cutter is abreast of thegear blank. In either case, when the cutter has made as many revolutionsas there are tooth spaces in the blank to be cut, the gear will befinished.

In Figs. 14 and 15, I have shown a cutter made according to a preferredembodiment of the invention for rough and finish cutting a tooth slot ina ingle revolution of the cutter in accordance with the principles ofthe'inventiorr- The cutter comprises a rotary head I" and a plurality'ofcutting segments I82 which are secured to the head by screws I83. KeysI84 which engage in spaced slots I85 in the head and seat against thebacks of the cutting segments serve to position the segments angularlyabout the axis of the head. In the embodiment shown, each of thesegments is provided with four integral cutting blades or teeth whichare relieved on their side and top faces. These cutting blades or teethmay be sharpened to have cutting ed es at both the gear blank when thisgap is abreast of the blank in the rotation of the cutter. The-segmentsbeginning with the segment Illa and including the segment denoted atIllb are provided with roughing blades or teeth. while the seg ments IBMto I820 inclusive are provided with finishing blades or teeth. Thefinishing blades have side, cutting edges of constant profile curvatureaccording to the'principles already given, the centers of the cuttingedgesof successive blades being disposed at progressively differentdistances from the am of the cutter- The finishing blades are also ofprogressively varying height and their top'eutting edges are accordinglyarranged in a spiral, such as indicated at I81, in accordance with theprinciples hereinbefore set forth.

The roughing blades are preferably arranged like a circular breach, thatis, they are preferably made of rogressively increasing height to theheight of the tooth space of the gear to be cut as a limit. The roughingblades may be and preferably are made with side cutting edges ofcircular arcuate curvature and. preferably the centers of curvature ofcorresponding successive side-cutting edges of the roughing blades areprogressively displaced from one another in a manner similar to thedisplacement of the centers of curvature of the side-cutting edges ofthe finishing blades. Thus, the roughing and finishing blades can berelief-ground in one continuous operation. Each roughing blade is.however,.

made of less thickness than the finishing blade which cuts at acorresponding point along the length of the tooth space of the gear.Thus stock will be left on the sides of the tooth space, after theroughing cut, to be finished in the finishing feed movement. Thus, asillustrated in Fig. 16, the roughing blade Illr which cuts at the largeend of the tooth space is narrower than the finishing blade I82] whichcuts at this same end of the tooth space.

In producing a tooth space of the gear blank, the cutter is adjustedinto engagement with the blank so that it will cut to the full depth ofthe tooth spaces of the blank without any feed in the direction of toothdepth. The roughing eut begins with the cutter center at Illb and Thereis, therefore, only a moderate amount of 7 stock required to be removedin the further roughin operation and therefore the rate of feed of thecutter may be accelerated to the point of reversal Illa. In the latterpart of this rough. ing feed, the rate of feed movement may be evengreater than the finishing feed. The finishing o eration takes place, asalready described, on the reverse movement while the cutter is being fedfrom Illa to lb. The stock. which has been left on the bottom of thesides of the tooth space at the small end thereof and which is denotedby the shaded area I03 in Fig.

during the time the first few roughing blades roughing blade of thecutter. After the roughing cuts-have reached the point Ill of the toothat the small end thereof, the feed movement may begin. At the pointwhere the roughing cuts have reached full height, the feed of the cutterwill have progressed to a point where its center is at I or to a pointwhere its center is between the positions I4! and IlIb.

ll: denotes the path of the cutting blade at the end of depth roughingwhen the cutter center is at Ill. From this point on, only the lowerpart of the sides of the tooth at the large end of the. tooth space needto be roughed out.

13, is removed during the finishing feed movement and the removal ofthis slight amount of stock helps to balance the cutting load of thelast finishing blade.

It is to be noted that with the cutter and method-described, the totalroughing cuts are included between the lines Ill and I" which divergefrom the small to the large ends of the tooth space. Likewise,successive roughing cuts diverge from the small to the large end of thetooth space so that the chips cut by the successive roughing blades areeach of increasing thickness from the small to the large end of thetooth. Inasmuch as the cutter rotation is in the direction of the arrowIll, it will be seen, then, that the roughing cut starts at the smallend of the tooth, that is, at the sides of reduced chip thickness. Thisis of advantage since it adds much to the life of the roughing blade,

for the life of any cutting blade is determined largely by the thickneaof the chip which it has to take at the beginning of its cut. I havetherefore devised a breaching operation for roughing tapered gears inwhich the stock is re-.

moved in tapered chips. The increase in chip thickness from the small tothe large end of seen thatthe above roughing method is bound to be veryefilcient in view of the long broachingcuts and tapering chipthicknesses.

If desired, the roughing cut may start with the cutter axis in aposition IlIc. The path of the first roughing blade will then be theline I60. It will be seen that this reduces the total chip thickness atthe small end of the tooth, which is the starting point of the chip,still further. Starting of the roughing cut with the tool center at someposition such as Illc or even to the left of lo is especially desirableif a tool is employed that has only roughing blades. In this case, theend position of depth roughing is to the left of the point Ill. In otherwords, full cutting depth is obtained before the cutter center hasreached position Ill.

As in my prior application, it will be noted that the finishing cuts inthe preferred direction of feed are along lines which extend from thetop of the teeth at the large end toward the bottom at the small end.This long finishing contact makes for smooth and accurate finishingcuts. This same inclined finishing contact is also obtained in thecutting of helical gears but in the case of these gears, the lines offinishing contact are oppositely inclined on opposite sides of the Bearteeth. a

of gears, but is here shown as applied to bevel gears. Here a pair ofdisc cutters are employed. One of them is a pure roughing cutter,constructed simply to remove stock. The other is a combination roughingand finishing cutter, which is made according to the principles of thisinvention as already described, and which is intended to finish thetooth slots previously roughed out by the other cutter.

The roughing cutter is denoted at 200. It may be of any suitableconstruction. In th embodiment shown, it is in the form of a slottingtool having a plurality of slotting blades or teeth arranged part-wayonly around its periphery. The blades of this cutter are preferably madeof progressively increasing height to cut deeper and deeper into theblank to the full height of a tooth space as a limit.

The slotting blades or teeth may be made in known manner, asillustrated. They are widest at their tips and have their opposite sidesconverging inwardly from their tips so as to clear the sides of thetooth slot being cut. One of the blades is shown in the sectional viewof Fig. 17 and is denoted at 2!. Fig. 19, which is a diagrammatic sideelevational view of the slotting cutter, indicates how the bladesincrease progressively in height around the periphery of the cutter. Thecutting portion of the cutter is denoted at 202. blades lie in a spiral204 and there is a gap 203 between the last and first blades.

The cutter 2I0, which does the finishing, is made according to theprinciples previously described, and, like the cutters previouslydescribed, contains preferably both roughing and finishing blades. Itmay be of the same general construction as any of the cutters previouslydescribed. The blades are arranged only part-way around the periphery ofthe cutter and preferably are made of progressively increasing height.In the diagrammatic view of Fig. 20, M2 denotes the cutting portion ofthe cutter and 2" denotes the spiral surface in which the tips of theroughing and finishing blades lie. There is a gap 2I3 between the lastfinishing and the first roughing blades of the cutter to permit ofindexing. This cutter has curved side-cutting edges determined inaccordance with the principles of the invention already set forth. Oneof the blades is shown in the sectional view at 2 in Fig. 1'7.

As will be noted from comparison of Figs. 19 and 20, the cutting portion202 of the roughing cutter 200 occupies a smaller part of the peripheryof that cutter than does the cutting portion 2I2 of the periphery of thecutter 2). This is because the slotting cutter 200 is preferably made sothat none of its blades will be cutting while the finishing blades ofthe cutter 2H1 are in operation. With this construction, the finalaccuracy and the final finish of the tooth surfaces produced upon a gearbeing out, are dependent solely upon the finishing blades of the cutter2l0 and are not affected in any way by the slot-1 ting cutter 200.

In use, the two cutters 200 and 2H! are rigidly connected to one anotherto rotate about a common axis 2i5, and they are spaced so that they willoperate in adjacent tooth spaces of the gear 2II which is to be cut. Thecutter 2H) is posi- As is seen, the tip surfaces of the tioned so thatit will be radial of the sear axis 2 l 8. The cutters are rotated inengagement with the gear blank while the blank is held stationary on itsaxis and, as the cutters rotate in en agement with the blank, they arefed first in one direction and then in the other across the face of theblank. During feed of the cutters in one direction, the cutter 20. slotsout a tooth space of the gear blank and the cutter 2i. completes theroughing of a tooth slot which has previously been operated upon by thecutter 200. During this feed movement, all the blades of the slottingcutter and all 01' the roughing blades of the cutter 2l0 will have takentheir cuts. On'the reverse feed movement. the gap 2 in the slottingcutter will be abreast of the gear blank and the finishing blades of thecutter 2" only will be in operation and will finish-cut the tooth spaceof the blank previously operated upon by the roughing blades of thiscutter. When the gap 2|! in this cutter comes abreast of the blank, theblank may be indexed. The gap 203 in the cutter 200 is long enough toregister with the gap zit also. The indexing movement is in thedirection of the arrow 2i! (Fig. 1'7).

The operation of the slotting tool is clearly illustrated in Fig. 18.Here a plurality of blades 2am, 20Ib, 20lc and 2lld are shown. The blade20la is one of the first blades to come into operation. The blade 20ldis one of the last. The blades are preferably of increasing height asindicated by the blades 20lb, 2lic and 20ld. It will be noted that it isonly the tip cutting edges of the blades which cut. The sides of theblades are inclined away from the sides of the tooth space and do nocutting. It is not necessary, therefore, to relieve them. The slottingcutter is, therefore, a very inexpensive tool and adds very little tothe total cost of the tool mechanism. At the same time, however, theoperation of cutting a gear blank can be speeded up considerably wheretwo cutters, such as shown, are employed or a smoother tooth surfacefinish and longer cutter life can be obtained.

In Fig. 17, the use of the two cutters is shown as applied to thecutting of a bevel sear blank. For cutting a spur gear blank, theprinciple is the same but the slotting cutter may be designed to reachfurther down into the tooth spaces of the blank and remove more stock.This is because the tooth spaces of a spur gear are of uniform widthfrom end to end and their sides do not converge like the sides of toothspaces of a bevel gear.

While several diiferent embodiments of the invention have beenillustrated and described. it will be understood that the invention iscapable of various further modifications and this application isintended to cover any variations, uses, or adaptations of the inventionfollowing, in general, the principles of the invention and includingsuch departures from the present disclosure as come within known orcustomary practice in the art to which the invention pertains and as maybe applied to the essential features hereinbei'ore set forth and as fallwithin the scope of the invention or the limits of the appended claims.

Having thus described my invention, what I claim is:

1. The method of producing a gear which comprises positioning a discmflling cutter, that has a plurality of radially disposed cutting bladeswhose corresponding side cutting edges have uniform profile curvaturebut varying inclination to a plane of rotation perpendicular to the axisof the cutter, in engagement with a gear blank, and cutting each toothof the blank by rotating said outter on its axis while producing arelative i'eed movement at a varying velocity between the cutter andblank longitudinally of the tooth in time with the cutter rotation sothat successive blades of the cutter cut at progressively difierentpoints from one end of the tooth to the other during a revolution of thecutter, and indexing the blank periodically.

2. The method of producing a gear which comprises positioning a discmilling cutter, that has a plurality of radially disposed cutting bladeswhose corresponding side cutting edges have uniform profile curvaturebut varying inclination to a plane of rotation perpendicular to the axisoi the cutter and which are arranged part way around its periphery witha gap between the last and the first blades, in engagement with a gearblank. and cutting each tooth of the blank by rotating said cutter onits axis while holding the blank stationary and while producing arelative feed movement between the cutter and blank longitudinally ofthe tooth in time with the cutter rotation so that successive blades 01'the cutter cut at progressively difi'erent points from one end of thetooth to the other during a revolution of the cutter, and indexing theblank when the gap in the cutter is abreast of the blank.

3. The method of producing a gear which comprises positioning a discmilling cutter, that has a plurality of radially disposed cutting bladeswhose corresponding side cutting edges have uniform profile curvatureand which are arranged part way only around its periphery with a gapbetween the last and the first blades, in engagement with a gear blank,and cutting the tooth spaces of the blank by rotating said cutter on itsaxis while holding the blank stationary and while producing a relativefeed movement at a varying velocity between the cutter and blanklongitudinally of the tooth space in time with the cutter rotation sothat successive blades of the cutter cut at progressivelydiflerentpoints from one end of the tooth space to the other during therelative feed movement, and indexing the blank when the gap in thecutter is abreast oi the blank.

4. The method of producing a gear which comprises positioning a discmilling cutter, that has a plurality of radially disposed cutting bladeswhich are of progressively varying height and whose corresponding sidecutting edges have uniform profile curvature. in engagement with a gearblank, and cutting each tooth space of the blank by rotating said cutteron its axis while producing a relative feed movement between the cutterand blank longitudinally of a tooth space in time with the cutterrotation and in a direction inclined to the root surface of the toothspace so that successive blades 01' the cutter cut at progressivelydifferent points from one end of the tooth space to the other during thefeed movement, and indexing the blank periodically.

5. The method of producing a gear which comprises positioning a discmilling cutter that has a plurality of radially disposed cutting bladeswhich are of progressively varying height and whose corresponding sidecutting edges have uniform profile curvature, in engagement with a gearblank, and cutting each tooth space of the blank by rotating said cutteron its axis while producing a relative feed movement between the cutterand blank longitudinally of the tooth space at a varying velocity in adirection inclined to the root surface of'the tooth space and in timewith the cutter rotation so that successive blades or the cutter cut atprogressively different points from one end of the tooth space to theother during the feed movement, and indexing the blank periodically.

- 6. The method oi producing a gear which comprises positioning a discmilling cutter, that has a plurality of radially disposed cuttingbladeswhich are of progressively varying height and whose corresponding sidecutting edges have uniform profile curvature and which are arranged partway only around its periphery with a gap between the last and firstblades, in engagement with a gear blank, and cutting each tooth space ofthe blank by rotating said cutter on its axis while holding the blankstationary and while producing a relative feed movement between thecutter and blank longitudinally of the tooth space and in a directioninclined to the root line of the tooth space in time with the cutterrotation so that successive blades of the cutter cut at progressivelydifferent points from one end or the tooth space to the other during thefeed movement, and indexing the blank when the gap of the cutter isabreast of the blank. v v

7. The method of producing a gear which comprises positioning a discmilling cutter, that has a plurality of radially disposed cutting bladeswhich are of progressively varying height and whose corresponding sidecutting edges have uniform profile curvature and which are arranged partway only around its periphery with a gap between the last and firstblades, in engagement with a gear blank, and cutting each tooth space ofthe blank by rotating said cutter on its axis while holding the blankstationary and while producing a relative feed movement at a varyingvelocity between the cutter and blank longitudinally of the toothspace'and in a direction inclined to the root line of the tooth space intime with the cutter rotation so that successive blades of the cuttercut at progressively different points from one end of the tooth space tothe other during the feed movement, and indexing the blank when the gapin the cutter is abreast of the blank.

8. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are 01' identical profilecurvature but are progressively displaced radially and axially of thecutter from one another, in engagement with a gear blank, and cuttingthe tooth spaces of the blank by rotating said cutter on its axis whileholding the blank stationary on its axis and while producing a relativefeed movement between the cutter and blank across the face of the blankin such timed relation to the cutter rotation that successive blades ofthe cutter cut at progressively difierent points from one end of thetooth space to the other during the feed movement, and indexing theblank periodically.

9. The method 01' producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical profilecurvature but are progressively displaced radially and axially oi thecutter from one another, in engagement with a gear blank, and cuttingeach tooth space of the blank by rotating said cutter on its axis whileholding the blank stationary on its axis and while producing.

a relative feed movement between the cutter and blank at a varyingvelocity across the face oi' t e b ank in such timed relation to thecutter rotation that successive blades of the cuttercut at progressivelydifferentpoints from one end of the tooth space to the other during thefeed movement, and indexing the blank periodically.

10. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical profilecurvature but are progressively displaced radially and axially of thecutter from one another, in 'engagement with a gear blank, and cuttingeach tooth space of the blank by rotating said cutter on its axis whileholding the blank stationary on its axis and while producing a relativefeed movement between the cutter and blank at a uniform velocity acrossthe face of the blank in such timed relation to the cutter rotation thatsuccessive blades of the cutter cut at progressively different pointsfrom one end of the tooth space to the other during the feed movement,and indexing the blank periodically. 11. The method of producing a gearwhich comprises positioning a disc milling cutter, which has a pluralityof radially disposed cutting blades whose corresponding side cuttingedges are of identical circular arcuate profile curvature but which havetheir centers of curvature progressively displaced radially and axiallyof the cutter from one another, in engagement with a gear blank, andcutting each tooth space of the gear by rotating said cutter on its axiswhile holding the blank stationary on its axis and while producing arelative feed movement between the cutter and blank across the face ofthe blank in such timed relation to the cutter rotation that successiveblades of the cutter cut at progressively different points from one endof the tooth space to the other during the feed movement, an indexingthe blank periodically.

12. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical circulararcuate profile curvature and which have their centers of curvaturedisplaced from one another radially and axially of the cutter, inengagement with a gear blank, and cutting each tooth space oi? the blankby rotating said cutter on its axis while holding the blank stationaryon its axis and while producing a relative movement between the cutterand blank at a varying velocity across the face of the blank in suchtimed relation to the cutter rotation that successive blades of thecutter out at progressively different points from one end of the toothspace to the other during the feed movement, and indexing theblank'periodically.

13. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposedcutting,blades whose corresponding side cutting edges are of identicalcircular arcuate profile curvature and which have their centers ofcurvature displaced from one another radially and axially 0f the cutter,in engagement with a gear blank, and cutting each tooth space of theblank by rotating saidcutter on its axis while holding theblankstationary on its axis and while producing a relative feed movementat a uniform velocity between the cutter and blank across the face ofthe blank in such timed relation to the cutter rotation that successiveblades of the cutter cut at progressively different points from one endof the tooth space to the other during the feed movement, and indexingthe blank periodically.

14. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical concavecircular arcuate profile curvature but which have their centers ofcurvature progressively displaced from one another uniform amountsradially and axially of the cutter, in engagement with a gear blank, andcutting each tooth space of the blank by rotating said cutter on itsaxis while holding the blank stationary on its axis and while producinga relative feed movement between the cutter and blank at a varyingvelocity across the face of the blank in such timed relation to thecutter rotation that successive blades of the cutter cut atprogressively different points from one end of the tooth space to theother during the feed movement, and indexing the blank periodically.

15. The method of producing a gear which comprises positioning a discmilling cutter, which has -a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical concavecircular arcuate profile curvature but have their centers of curvatureprogressively displaced varying amounts from one another radially andaxially of the cutter, in enagement with a gear blank, and cutting eachtooth space of the blank by rotating said cutter on its axis whileholding the blank stationary on its axis and while producing a relativefeed movement at a uniform velocity between the cutter and blank acrossthe face of the blank in such timed relation to the cutter rotation thatsuccessive blades of the cutter cut at progressively different pointsfrom one end of the tooth space to the other during the feed movement,and indexing the blank periodically.

16. The method of producing a gear which comprises positioning a discmilling cutter, which has a plurality of radially disposed cuttingblades whose corresponding side cutting edges are of identical concavecircular arcuate pro-file curvature but have their centers of curvatureprogressively displaced from one another varying amounts radially andaxially of the cutter, in engagement with a gear blank, and cutting eachtooth space of the blank while rotating said cutter on its axis andwhile producing a relative feed movement at a varying velocity betweenthe cutter and blank across the face of the blank in such timed relationto the cutter rotation that successive blades of the cutter cut atprogressively different points from one end of the tooth space to theother during the feed movement, and indexing the blank periodically.

1'1. The method of cutting a tapered gear which comprises positioning arotary d sc gear cutter, which has a plurality of radially disposedcutting blades whose corresponding side-cutting edges are of identicalconcave circular arcuate profile curvature but have their centers ofcurvature progressively displaced from one another, in engagement with atapered gear blank, and cutting each tooth space of the blank byrotating said cutter on its axis while producing a relative feedmovement between the cutter and blank longitudinally of the tooth spacein the direction of the root line of the tooth space, and index'ng theblank periodically.

18. The method of cutting a gear which comprises positioning a rotarydisc cutter, that has a plurality of cutting blades of concave profileshape arranged part way only around its periphery with a gap between thelast and first blades, in engagement with a gear blank and cutting eachtooth space of the blank by rotating said cutter on its axis whileproducing a relative feed movement between the cutter and blank acrossthe face of the blank at a varying velocity in time with the cutterrotation so that successive blades of the cutter cut at progressivelydifferent points from one end of the tooth space to the other, andindexing the blank when the gap in the cutter is abreast of the blank.

19. The method of cutting a gear which comprises employing a pair ofcoaxially mounted disc cutters, each of which has a plurality of cuttingblades arranged part way around its periphery with a gap between thelast and first blades, one of the cutters having roughing blades onlyand the other cutter having both roughing andfinishing blades, and theroughing cutter having a gap of sufiicient angular extent to registersimultaneously with both the finishing blades of the finishing cutterand the gap in said cutter, positioning said cutters in engagement witha gear blank so that they will operate simultaneously in two adjacenttooth spaces of the blank, and rotating said cutters in engagement withthe blank while producing a relative feed movement between the cuttersand blank across the face of the blank in time with the rotation of thecutters, and indexing the blank when the gaps in the two outters areabreast of the blank.

20. The method of cutting a tapered gear which comprises positioning arotary cutter, which has a plurality of radially disposed cutting bladesof progressively varying height arranged'around its periphery, inengagement with a tapered gear blank, and cutting each tooth space ofthe blank by rotating said cutter on its axis while producing arelativefeed movement between the cutter and blank longitudinally of thetooth space in such timed relation to the cutter rotation that thesuccessive blades of the cutter cut progressively from one end of thetooth space to the other and the blade which is of smaller height cutsat the large end of the tooth space, and indexing the blankperiodically.

21. The method of cutting a gear which comprises positioning a rotarycutter, which has a plurality of radially disposed cutting blades ofprogressively varying height whose corresponding side cutting edges areof constant profile curvature but are progressively displaced relativeto one another laterally and radially of the axis of .the cutter, inengagement with a gear blank, and cutting each tooth space of the blankby rotating said cutter on its axis while producing a relative feedmovement between the cutter and blank longitudinally of the tooth spacein such timed relation to the cutter rotation that the blades ofsmallest height cut at the large end of the tooth space and succeedingblades cut progressively along the length of the tooth space toward thesmall end thereof, and indexing the blank periodically.

22. The method of cutting a tapered gear which comprises positioning arotary cutter, that has a plurality of radially disposed cutting bladeswhose corresponding side cutting edges are of constant profile curvaturebut are progressively displaced relative to one another at a uniformrate both laterally and radially of the cutter axis, in engagement witha gear blank, and cutting each tooth space of the blank by rotating saidcutter on its axis while producing the relative feed movement betweenthe cutter and blank longitudinally of the tooth space in such timedrelation to the aasmsa cutter rotation that thecutting edge of thecutter which is the least displaced from the cutter axis cuts at thelarge end of the tooth space and the cutting edges of successive bladescut progressively along the length of the tooth space toward the smallend thereof during the feed movement, and indexing the blankperiodically.

23. The method of cutting a tapered gear which comprises positioning arotary cutter, that has a plurality-oi! radially disposed cutting bladeswhose corresponding side cutting edges are of constant profile curvaturebut are progressively displaced relative to one anther at a non-uniformrate both radially and axially of the cutter axis, in engagement with atapered gear blank, and cutting each tooth space of the blank byrotating the cutter on its axis while producing a relative feed movementbetween the cutter and blank longitudinally of the tooth space in suchtimed relation to the cutter rotation that the cutting edge which isleast displaced trim the cutter axis cuts at the large end of the toothspace and successive cutting edges cut progressively along the lengthoi. the tooth space to the small end thereof, and indexing the blankperiodically.

24. The method of cutting a tapered gear which comprises positioning arotary cutter, that has a plurality of radially disposed cutting bladesof progressively varying height whose corresponding side cutting edgesare of constant profile curvature but are progressively displaced fromone another at a uniform rate laterally and radially oi the cutter axis,in engagement with a tapered gear blank and cutting each tooth space ofthe blank by rotating said cutter on its axis while producing a relativefeed movement at a varying rate between the cutter and blanklongitudinally of the tooth space in time with the cutter rotation andin a'direction inclined to the root line of the tooth space, andindexing the blank periodically.

25. The method of cutting a tapered gear which comprises positioning arotary cutter, that has a plurality of radially disposed .cutting bladesof progressively varying height whose corresponding side cutting edgesare of constant profile curvature but are progressively displacedrelative to one another at a non-uniform rate both laterally andradially of the cutter axis, in engagement with a tapered gear blank,and rotating said outter on its axis while producing a relative feedmovement at a uniform rate between the cutter and blank longitudinallyof the tooth space in time with the cutter rotation and in a directioninclined to the root line of the tooth space, and dexing the blankperiodically.

26. The method of cutting a tapered gear which comprises positioning arotary cutter, which has a plurality of radially disposed cutting bladesof progressively varying height whose corresponding side cutting edgesar of constant profile curvature but are progressively displacedrelative to one another at a non-uniform rate both laterally andradially of the cutter axis, in engagement with a tapered gear blank,and cutting each tooth space of the blank by rotating said cutter on itsaxis while producing a relative feed movement between the cutter andblank at a nonuniform rate longitudinally of the tooth space in timewith the cutter rotation and in a direction V inclined to the root lineof the tooth space, and

indexing the blankperiodically.

27. The method of cutting a tapered gear which comprises positioning arotary cutter, that has a plurality of radially disposed blades whosecorrespace and on its axis and plurality of saw,

sponding side cutting edges are of circular arcuand have equal radii ofcurva ture but have their centers of curvature arranged of the cutter ona three-dimenwith a taperedgear blank, and cutting each tooth space ofthe blank axis while producing a relative feed movement between thecutter and blank longitudinally of the tooth space in such timedrelation with the cutter rotation that the side cutting edge, whosecenter is on the part of the spiral which is of smallest lead, cuts atthe large end of the tooth successive cutting dges cut progres- 28. Themethod of cutting a tapered gear which comprises positioning a rotarycutter, that has a plurality of radially disposed roughing blades ofprogressively increasing height followed by a plurality of radiallydisposed finishing blades of progressively increasing height, inengagement with a gear blank, and cutting each tooth space of the blankby rotating said cutter on its axis while simultaneously producing arelative feed movement between the cutter and blank across the face ofthe blank which is in one direction whilethe roughing blades are cuttingand in the opposite direction while the finishing blades are cutting,the rotation of the cutter being so .00- ordinated to the relative feedmovement that the finishing blade which is of greatest height cuts atthe small end of the tooth space of the blank, and indexing the blankperiodically.

29. The method of cutting a gear which comprises employing a rotary disccutter that has a plurality of radially arranged cutting blades whoseopposite side-cutting edges are symmetrically disposed with reference toa plane of rotation perpendicular to the axis of the cutter and whosecorresponding side-cutting edges have the same concave profile shape buthave profiles progressively displaced relative to one another at auniform rate laterally and radially of the cutter axis, and rotatingsaid cutter in engagement with a gear blank while holding the blankstationary on its axis and while producing a relative reciprocatory feedmovement at a varying velocity between the cutter and blank across theface of the blank in time with the cutter rotation so that the ciittermakes one revolution for'each feed reciprocatlon, and periodicallyindexing the blank.

30. The method of cutting a gear which comprises employing a rotary disccutter that has a plurality of radially arranged cutting blades whoseo'pposite side-cutting edges are symmetrically with reference to a planeof rota tion pe ndicular to the axis of the cutter and whosecorresponding side-cutting edges have the same concave profile shape buthave .proflles progressivcfy -adisplaced relative to one another at avarying rate laterally and radially of the cutter axis, and rotatingsaid cutter in engagement with a gear blank while holding the blankstationary while producing a relative reciprocatory feed movement at auniform velocity between the cutter and blank across the face of theblank in time with the cutter rotation so that the cutter makes arevolution for each feed reciprocation. and periodically indexing theblank.

31. The method of cutting a gear which comprises employing a rotary disccutter that has a radially arranged cutting blades whose oppositeside-cutting edges are symmetriincreasing-lead, in engagement.

by rotating said cutter on its tion perpendicular cally disposed withreference to a plane of rotato the axis of the cutter and whosecorresponding'side-cutting edges have the sameconcave profile shape buthave profiles progressively displaced relative to oneanother at avarying rate laterally'and radially of the cutter axis, and rotatin saidcutter. inengagement with a gear stationary on its axis and whileproducing a relative reclprocatory feed movement at a varying velocitybetween the cutter and blank across .the face of the blank in time withthe cutter rotation so that the cutter makes a revolution for each feedreciprocation, and'periodically indexing the blank.

32. The method of cutting a gear which comprises employing a rotary disccutter that has a plurality of radially arranged cutting blades whichare of progressivelyvarying height, whose opposite side-cutting edgesare symmetrically disposed with reference to a plane of rotationperpendicular to the axis of the cutter and whose correspondingside-cutting edges have the same concave profile shape but have profilesprogressively displaced relative to one another at a uniform ratelaterally and radially of the cutter axis, and rotating said cutter inengagement with a gear blank while holding the blank stationary onitsaxis and while reducing a relative reciprocatory feed movement at avarying velocity between the cutter and blank across the face of theblank in a direction inclined to the root surface of the'blank in timewith the cutter rotation, so that the cutter makes a revolution forpendicular to the axis of the cutter and whose correspondingside-cutting edges have the same concave profile shape but have profilesprogressively displaced relative to one another at a varyand radially ofthe cutter axis,

on its axis and relative reciprocatory feed movement at a uniformvelocity between the cutter and blank across the face of the blank in adirection inclined to the root surface of the blank in time with thecutter rotation so that the cutter makes a revolution for each feedreciprocation, and periodically indexing the blank.

34. The method of cutting a gear which comprises employing a rotary disccutter that has a plurality of radially arranged cutting blades whichare of progressively varying height, whose opposite side cutting edgesare symmetrically disposed with reference to a plane of rotationperpendicular to the axis of the cutter and whose correspondingside-cutting edges have the same concave profile shape but have profilesprogressively displaced relative to one another at a varying ratelaterally and radially of the cutter axis, and rotating said cutter inengagement with a ear blank while holding the blank stationary on itsaxis and while producing a relative reciprocatory feed movement at avarying velocity between the cutter and blank across the face of theblank in a direction inclined to the root surface of the blank in timewith the cutter rotation so that blank while holding the blank cutting agear which com-- a plane of rotation per- I the cutter makes arevolution for each feed reciprocatlon, and periodically indexing theblank 35. The method of producing a gear which comprises employing arotary disc cutter that has a plurality of radially arranged cuttingblades which are progressively varying height, whose tooth space of theblank by rotating said cutter in engagement with the blank while holdingthe blank stationary on its axis and while producing a relativereciprocatory feed movement between the cutter and blank at a varyingvelocity across the face oi the blank in a direction inclined to theroot surface of the tooth space in such timed relation to the cutterrotation that successive blades of the cutter cut at progressivelydifierent points from one end of the tooth space to the other during thefeed movement, and periodically indexing the blank.

36. The method oi producing a gear which comprises employing a rotarydisc cutter that has a plurality of radially arranged cutting bladeswhich are of progressively varying height, whose opposite side-cuttingedges are symmetrically disposed with reference to a plane of rotationperpendicular to the axis of the cutter and whose correspondingside-cutting edges are of identical concave circular arcuate profilecurvature but have their centers of curvature progressively displacedvarying amounts from one another radially and axially oi the cutter, andcutting each tooth space oi the blank by, rotating said cutter inengagement with the blank while holding the blank stationary on its axisand while producing a relative feed movement at a unitorm velocitybetween the cutter and blank across the face oi the blank in a directioninclined to the root line oi the tooth space and in such timed relationto the cutter rotation' that successive blades of the cutter cut atprogressively diiierent points from one end of the tooth space to theother during the feed movement, and indexing the blank periodically.

3'7. The method of producing a gear which comprises positioning a rotarydisc cutter that has a plurality of radially disposed cutting bladeswhich are of progressively varying height, whose opposite side-cuttingedges are symmetrically disposed with reference to a plane of rotationperpendicular to the axis of the cutter and whose correspondingside-cutting edges are of identical concave circular arcuate profilecurvature but have their centers oi curvature progressively displacedfrom one ano her varying amounts radially and axially oi the cutter, andcutting each tooth space of the gear blank by rotating said cutter inengagement with the blank while holding the blank stationary on its axisand while producing a relative feed movement at a varying velocitybetween the cutter and blank across the face of the blank in a directioninclined to the root surface of the tooth space and in such timedrelation to thecutter rotation that successive blades of the cutter cutat progressively different points from. one end of the tooth space tothe other during the feed movement, and indexing the blank periodically.

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